Prove that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures. (10 points)

Theorem : Opposite sides of a parallelogram are congruent or equal.

Let us suppose a parallelogram ABCD.  

Given: and  (According to the definition of parallelogram)

We have to prove that: AB is congruent to CD and BC is congruent to AD.

Prove: let us take two triangles,  and

In these two triangles,  { By the definition of alternative interior angles}

Similarly,                        

And,                                AC=AC (common segment)

By  ASA,  

thus By the property of congruent triangle, we can say that corresponding  sides of  are also congruent.

Thus, AB is congruent to CD and BC is congruent to AD.

Step-by-step explanation:

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